Vaccination is the primary intervention for controlling the spread of infectious diseases. A certain level of vaccination rate (referred to as "herd immunity'') is needed for this intervention to be effective. However, there are concerns that herd immunity might not be achieved due to an increasing level of hesitancy and opposition to vaccines. One of the primary reasons for this is the cost of non-conformance with one's peers. We use the framework of network coordination games to study the persistence of anti-vaccine sentiment in a population. We extend it to incorporate the opposing forces of the pressure of conforming to peers, herd-immunity and vaccination benefits. We study the structure of the equilibria in such games, and the characteristics of unvaccinated nodes. We also study Stackelberg strategies to reduce the number of nodes with anti-vaccine sentiment. Finally, we evaluate our results on different kinds of real world social networks.